• Introduction to the present project
• Objectives of the current research
• Background and Context
• Research Questions
• Data sources
• Methods - Spatial data are special!
• Methods - The INLA approach to Bayesian analysis
• Results & visualizations
• Wrap up and current work

• Women in Latin America face violence in many form in daily life
  • Daughters, sisters, wives; working or retired
• Machismo and Marianismo are cultural traditions found throughout Latin America
  • Stress the persistent conflict between being "manly" and being "pure and passive"
  • Often leads to conflict within households & domestic violence
  • Absolutely not unique to Latin America

• La cultura de violencia
• In Mexico, 44% of women have suffered some type of violence from their partner. Report
• This often results in some form of internal displacement for women and men
  • Attempting to leave this violence behind and seek asylum
  • Women are often targeted for violence by cartels or gangs

• Spatial poverty traps
  • Areas where poverty is persisently high over both time and space
  • These are areas where physical, natural, social, political, and human capital is low and poverty is high
  • Different disciplines provide large amount of evidence on linking poverty and gender based violence
• The contextual factors related to gender based violence are not only socioeconomic factors
  • Such as poverty or low education
  • Also include cultural and demographic patterns mainly in some rural or remote areas of the country

• Provide insights into the association between poverty in Mexico and gender-based violence
• Identify significant concentrations of high poverty rates and high incidence of gender based violence

• Are poverty and female homicide co-incident in Mexico?
• Is this relationship stationary over time and space?

• The information for homicides comes from the vital statistics of the Instituto Nacional de Estadistica y Geografia (INEGI)
  • These data are individual death records
  • Using ICD-10 codes, we isolate female homicides (ICD-10: X85-Y09)
  • Between years 1995 and 2015: a total of 15,108 homicides
  • Construct homicide rates by age (5 year age categories), year and municipio of occurrence
  • This generates a total of 1,759,248 rates over the period of study
  • Standardize all age-specific rates to Mexican national age structure in 2010 and sum rates within municipio and year to arrive at age-standardized rates

• Total homicide rates over time

1990 Poverty Rates

2010 Poverty Rates

*Chihuahau over time

• Several indicators are used in the analysis to control for physical and socioeconomic environment of municipios
  • Distance to US border
  • Poverty quartile
  • Migration intensity
  • % of population with incomplete primary school
  • Masculinity index
  • % population that is married
  • Average age at first union
  • Altitude

• I specify a Bayesian Hierarchical model for the standardized mortality ratio

• \[Y_{ij} \sim \text{NegBin} (\lambda_{ij} \text{E}_{ij}, \lambda+\lambda^2/\theta)\]
• \[ln \lambda_{ij} = \beta_{0} + x'\beta +\text{poverty}_i*\text{time}_t+\gamma_j*poverty_i + u_j + v_j\]
• \[\gamma_1*\text{time} + \gamma_2* \left ( \text{time} * poverty_i \right )+\gamma_3*(\text{time} * seg_i)\]
• \[\gamma_j \sim \text{CAR}(\bar \gamma_j, \tau_{\gamma}/n_j)\]
• \[u_j \sim \text{CAR}(\bar u_j, \tau_u /n_j)\]

• \[v_j \sim \text{N}(0, \tau_v )\]

• Vague Gamma priors for all the \(\tau\)'s

• Vague Normal priors for all the fixed effect \(\beta\)'s and \(\gamma\)'s

• This type of model is commonly used in epidemiology and public health
• Various types of data likelihoods may be used
• Need to get at:

*\[p(\theta|y) \propto p(y|\theta)p(\theta)\]

• Traditionally, we would get \(p(\theta|y)\) by:
  • either figuring out what the full conditionals for all our model parameters are (hard)
  • Use some form of MCMC to arrive at the posterior marginal distributions for our parameters (time consuming)

• Integrated Nested Laplace Approximation - Rue, Martino & Chopin (2009)
• One of several techniques that approximate the marginal and conditional posterior densities
  • Laplace, PQL, E-M, Variational Bayes
• Assumes all random effects in the model are latent, zero-mean Gaussian random field, \(x\) with some precision matrix
  • The precision matrix depends on a small set of hyperparameters
• Attempts to construct a joint Gaussian approximation for \(p(x | \theta, y)\)
  • where \(\theta\) is a small subset of hyper-parameters

• Apply these approximations to arrive at:

• \(\tilde{\pi}(x_i | y) = \int \tilde{\pi}(x_i |\theta, y)\tilde{\pi}(\theta| y) d\theta\)

• \(\tilde{\pi}(\theta_j | y) = \int \tilde{\pi}(\theta| y) d\theta_{-j}\)

• where each \(\tilde{\pi}(. |.)\) is an approximated conditional density of its parameters

• Approximations to \(\pi(x_i | y)\) are computed by approximating both \(\pi(\theta| y)\) and \(\pi(x_i| \theta, y)\) using numerical integration to integrate out the nuisance parameters.
  • This is possible if the dimension of \(\theta\) is small.
• Approximations to \(\tilde{\pi}(\theta|y)\) are based on the Laplace appoximation of the marginal posterior density for \(\pi(x,\theta|y)\)
• Their approach relies on numerical integration of the posterior of the latent field, as opposed to a pure Gaussian approximation of it

• Protective effects on female homicide risk: Shorter distance to border, Higher level of education, higher proportion married, older age at first union

• Risk factors: High poverty areas farther from the US border

• General hypothesis tests: Poverty displays a constant risk factor for female homicide over time - consistent temporal effect

• Poverty displays little variation in how it impacts female homicide over space - consistent spatial effect

• There are several persistent areas of spatial clustering in the northwest of the country
  • Chihuahua, Durango and Sinaloa
  • as well as the southwest in states of Oaxaca, Michoacan, Gurrero and Estado de Mexico.
• No space-time significance of poverty
• Poverty is time invariant

• Current work is focusing on estimating influence of violence on life expectancy over time
• Multi-level analysis focusing on incorporating individual level factors with contextual information
• Exploring other causes of death in the data for spatial and temporal patterns

corey.sparks@utsa.edu

Coreysparks1

UTSA Demography